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# Risk and Return

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Because of the risk-return tradeoff, you must be aware of your personal risk tolerance when choosing investments for your portfolio. Taking on some risk is the price of achieving returns; therefore, if you want to make money, you can't cut out all risk. The goal instead is to find an appropriate balance - one that generates some profit, but still allows you to sleep at night.

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### Risk and Return

1. 1. Lecture 10 Return and Risk
2. 2. Rates of Return  A key measure of investors’ success is the rate at which their funds have grown  Holding-period return (HPR) of shares is composed of capital gain and dividend  RH = (C)+ (PE-PB) /PB  This definition assumes end of period returns and ignores re-investment of income
3. 3.  Return Relative It is a different way to calculate return. This method is used when a cumulative wealth index or a geometric mean has to be calculated. Return Relative (RR)= C+PE/PB Rates of Return
4. 4. Rates of Return  Dividend Yield = Percentage return from dividends i.e. (D/PB)x100  To calculate HPR over a period of time, we can use:  Arithmetic average  Geometric average  Dollar weighted return
5. 5. Arithmetic Average  It is the sum of periodic return divided by number of periods  Arithmetic Average = 15/3 = 5% Period 1 10% Period 2 25% Period 3 -20% Sum 15%
6. 6. Geometric Average nth root of the product of returns for n years Geometric mean = (1+R1)x(1+R2)x(1+R3)1/n – 1  = [(1+10%) x (1+ 25%) x(1+(-20%))] 1/3 – 1  [(1.1) x (1.25) x (.8)] 1/3 – 1  (1.1) 1/3 – 1  1.03-1  .03 or 3%
7. 7. Problem with Arithmetic average  Suppose the following:  Calculating arithmetic mean gives false value of 25% return = (100%-50%)/2  And geometric = (1+1)x(1-.5)1/2 - 1  =1-1 = 0% Year Begin value Ending value HPR 2007 50 100 100% 2008 100 50 -50%
8. 8. Geometric Vs Arithmetic  In highly volatile security prices, arithmetic mean is biased upward and we should use geometric mean  If rates of returns are the same for all years, geometric and arithmetic averages gives same results
9. 9. Taking a Global  When investors buy or sell securities in other countries, they also take exchange rate risk or currency risk  Fluctuation in currency value can be either a source of loss or profit  If the foreign currency strengthens, your returns will increase or vice versa
10. 10. An Example  Suppose you purchased 100 shares of IBM at NYSE for \$300 each. The dollar-rupee parity was 60 rupees a dollar at the that time. So your total investment in rupees was 100x\$300 = \$30000 x 60 =Rs.1800,000  At the end of the year, IBM share price was \$310, giving you \$10 profit per share, your profit is = 100 x 10 = \$1000x60 = Rs.60000  But the dollar-rupee parity had jumped to 78 rupee a dollar, now your total investment is =100x310 = \$31000 x 78 = Rs.2418000  And your profit is 2,418,000-180,0000 = Rs.618,000  Or in percentage = 618,000/1800,000 = .343 or 34%
11. 11. Equation for calculating returns from foregin stocks  = [(P1/Po)x(C1/Co)] – 1  [(310/300)x(78/60)] – 1  [(1.03) x (1.3)] – 1  1.339 – 1  0.339 or 34%  P1 = Ending share price  Po = Beginning share price  C1 = Ending value of domestic currency  Co = Beginning value of domestic currency
12. 12. Risk  Any investment involves some degree of uncertainty about future returns  Risk arises out of variability in returns  If an asset has no variability in returns, the assets is considered to be risk free like one year T-bills
13. 13. Type of Risk Systematic Risk (Not diversifiable)  Market Risk  Interest Rate Risk  Purchasing Power Risk Unsystematic Risks (Diversifiable)  Business Risk  Financial risk
14. 14. Sources of Risk  Market risk : variability in returns due to fluctuations in aggregate market  Recession, wars etc  Interest Rate Risk Interest risk refers to variability of total returns, particularly on fixed income securities due fluctuation in Interest rates.  Purchas Power or Inflation risk  when purchasing power declines.  Inflation also leads to hike in interest rates because lenders demand more to compensate themselves for loss in purchasing power
15. 15.  Exchange risk = for international investors, a source of risk come from exchange rate fluctuation  Country Risk = For international investors, economic and political stability, law and order situation are important consideration in the investment decision Sources of Risk
16. 16. Interest rates and returns  1. Increase in interest rates increases the required rate of return  RRR= Rf + Risk premium which reduces the prices of the securities (intrinsic value)  2. It increases cost of borrowing and hence cost of capital  3. It reduces money supply which lower demand for securities and resultantly prices fall. RRR Cashflow alueIntrinsicV + = 1
17. 17. Measuring Risk  The most commonly used measure of risk for securities is standard deviation  SD measure the total risk of a security or a portfolio  It measure deviations of each observation from the arithmetic mean 1 ]R-[R 1 2 _ i − = ∑= n n i σ Measuring Risk
18. 18. Standard Deviation 89.5 4 139 15 139 == − 1 ]R-[R 1 2 _ i − ∑= n n i
19. 19. Interpretation  The 5.89 SD means that the security return can fluctuate between +/-5.89 from the mean value of 16%  More specifically, the return can fluctuate between 16 - 5.89 = 10.11 or 16 + 5.89 = 21.89 Your return could fall to as low as 10.11% or could rise to 21.89 %
20. 20. Realized Returns and risk from Investing Class of assets Average SD S&P 500 Composite 9.21% 19.75% S&P Industrial 9.66 21.57 S&P Utility 8.47 20.54 Small Cap Stock (S&P 600) 14.82 37.23 AAA 20-year Corp Bond 3.87 10.05 US 15-year Bond 3.25 10.22 T-Bills 1.569 4.65
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